The purchase last year of Italian fashion house Gianfranco Ferre by Dubai-based retailer Paris Group has been heavily scrutinized since the departure last year of Ferre’s designers and top executives.

Now, the new owner’s commitment could come under fire again: Ahmed Sankari, the new chief executive and son of the Paris Group owner, will not attend Ferre’s fashion show during Milan Fashion Week Monday.

Mr. Sankari had planned to fly from Dubai to Milan to for the runway show, according to a spokesman for the company. But just days before the show, Mr. Sankari canceled his trip, the spokesman said, without providing more details.